Is achieving a basic skill level related to the location of the school? The resu

Question

Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At alpha equals 0.05 , test the hypothesis that the variables are independent. Complete parts (a) through (d). Subject Location Reading Math Science Urban 43 47 40 Suburban Suburban 62 64 50 (a) Identify the claim and state the null and alternative hypotheses. Upper H 0 H0: Skill level in a subject is independent of location. Upper H Subscript a Ha: Skill level in a subject is dependent on location. The null hypothesis is the claim. (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? d.f. equals = 2 2 Find the critical value. chi Subscript 0 Superscript 2 20 equals = 5.991 (Round to three decimal places as needed.) Choose the correct rejection region below. A. chi squared 2 greater than or equals chi Subscript 0 Superscript 2 20 B. chi squared 2 less than or equals chi Subscript 0 Superscript 2 20 C. chi squared 2 less than < chi Subscript 0 Superscript 2 20 D. chi squared 2 greater than > chi Subscript 0 Superscript 2 20 Your answer is correct. (c) Calculate the test statistic. If convenient, use technology. chi squared 2 equals = ? (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

a) Ho: Skill level in a subject is independent of location

Ha:  Skill level in a subject is dependent on location.

b) degree of freedom =(number of rows-1)*(number of columns-1) =(3-1)*(2-1)=2

critical value at 0.05 level =5.991

rejecttion region : hi squared 2 greater than or equals 5.991

c) applying chi sqaure test of independence:

from above test stat =0.243

Observed O reading math science Total urban 43 47 40 130 suburban 62 64 50 176 Total 105 111 90 306 Expected E=rowtotal*column total/grand total reading math science Total urban 44.608 47.157 38.235 130 suburban 60.392 63.843 51.765 176 Total 105 111 90 306 chi square =(O-E)^2/E reading math science Total urban 0.058 0.0005 0.0814 0.140 suburban 0.043 0.000 0.060 0.103 Total 0.101 0.001 0.142 0.243

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